Date of Award
Spring 1991
Document Type
Thesis - Restricted
Degree Name
Master of Science (MS)
Department
Biomedical Engineering
First Advisor
Myklebust, Joel
Second Advisor
Krenz, Gary
Third Advisor
Ropella, Kristina M.
Abstract
The correlation dimension has been used to characterize the effect of anesthesia on the EEG [13][14][22], epileptic discharges [1], and mental activity [16]. Although the methods are computationally intensive, the resulting data reduction permits simplification of presentation, and thereby the possibility of more direct identification of EEG pathology and changes in state. In the following study, dimensional analysis is used to characterize the human electroencephalogram and to determine whether it can be presented as a chaotic time series. The novelty in this research lies in the method of presenting the results; they are presented in a topographical mapping across the scalp. Additionally, the validity of using short epochs for dimensional calculations is evaluated. Chapter 1 provides a historical background about chaos and dynamical systems, followed by a description of strange attractors and their sensitive dependence on initial conditions. Chapter 2 introduces the dimension of dynamical systems and discusses different methods for computing the dimension of a time series. Chapter 3 presents a study of low dimensional systems. Two models are analysed: The Henon map, and the Lorenz attractor. Chapter 4 discusses the applications of dimensional analysis to EEG. The chapter starts with an introduction to EEG, its sources, its recording, and its characteristics. Then, the dimensionality of the human EEG is addressed using embedded time series. First, the effect of the lag factor on the embedding of the time series is investigated. Then, spatial and temporal dimensional analyses are performed on the EEG data and the results are presented in a topographical mapping across the scalp. Additionally, the effect of the number of data points analysed on the dimension of the time series and the validity of short data segments are evaluated. The results are given in Appendices D and E. Finally, Chapter 5 summarizes and concludes the results of this study. A listing of the software for implementing the correlation dimension of experimental time series is provided in Appendices A and B.
Recommended Citation
Abu-Faraj, Ziad U., "Characterization of the Electroencephalogram As a Chaotic Time Series" (1991). Master's Theses (1922-2009) Access restricted to Marquette Campus. 3884.
https://epublications.marquette.edu/theses/3884